Formal studies of learning abstract grammars have, for decades, yielded deep results, some practical applications and quite a lot of fun. But no one believes that children learn the grammar of their native language independent of meaning (semantics) and use (pragmatics). Recent results suggest that is now possible, although still very difficult, to build computational and formal models of how children learn language. This paper will review some recent developments in computational modeling of language acquisition and suggest how they might be extended to grammatical inference.